Question

Consider a linear homogeneous system of equations Ax = 0, where A is an $n \times n$ matrix, x is an $n \times 1$ vector and 0 is an $n \times 1$ null vector. Let r be the rank of A. For a non-trivial solution to exist, which of the following conditions is/are satisfied?

• A. Determinant of A = 0
• B. r = n
• C. r < n
• D. Determinant of A ≠ 0

Official answer: A. Determinant of A = 0; C. r < n